Introduction

Map projections are attempts to portray the surface of the earth
or a portion
of the earth on a flat surface. Some distortions of
conformality, distance,
direction, scale, and area always result from this process. Some
projections
minimize distortions in some of these properties at the expense
of maximizing
errors in others. Some projection are attempts to only
moderately distort
all of these properties.

Conformality

When the scale of a map at any point on the map is the same
in any direction,
the projection is conformal. Meridians (lines of longitude)
and parallels
(lines of latitude) intersect at right angles. Shape is
preserved locally
on conformal maps.

Distance

A map is equidistant when it portrays distances from the
center of the
projection to any other place on the map.

Direction

A map preserves direction when azimuths (angles from a point
on a line
to another point) are portrayed correctly in all directions.

Scale

Scale is the relationship between a distance portrayed on a
map and the
same distance on the Earth.

Area

When a map portrays areas over the entire map so that all
mapped areas
have the same proportional relationship to the areas on the
Earth that
they represent, the map is an equal-area map.

Different map projections result in different spatial
relationships between
regions.

Selected Map Projections

Cylindrical Projections

Cylindrical Equal Area

Cylindrical Equal-Area projections have straight meridians and
parallels,
the meridians are equally spaced, the parallels unequally
spaced. There
are normal, transverse, and oblique cylindrical equal-area
projections.
Scale is true along the central line (the equator for normal,
the central
meridian for transverse, and a selected line for oblique) and
along two
lines equidistant from the central line. Shape and scale
distortions increase
near points 90 degrees from the central line.

Behrmann Cylindrical Equal-Area

Behrmann's cylindrical equal-area projection uses 30:00
North as the parallel
of no distortion.

The Mercator projection has straight meridians and parallels
that intersect
at right angles. Scale is true at the equator or at two
standard parallels
equidistant from the equator. The projection is often used for
marine navigation
because all straight lines on the map are lines of constant
azimuth.

The Miller projection has straight meridians and parallels
that meet at
right angles, but straight lines are not of constant azimuth.
Shapes and
areas are distorted. Directions are true only along the
equator. The projection
avoids the scale exaggerations of the Mercator map.

Oblique Mercator projections are used to portray regions along
great circles.
Distances are true along a great circle defined by the tangent
line formed
by the sphere and the oblique cylinder, elsewhere distance,
shape, and
areas are distorted. Once used to map Landsat images (now
replaced by the
Space Oblique Mercator), this projection is used for areas
that are long,
thin zones at a diagonal with respect to north, such as Alaska
State Plane
Zone 5001.

Transverse Mercator projections result from projecting the
sphere onto
a cylinder tangent to a central meridian. Transverse Mercator
maps are
often used to portray areas with larger north-south than
east-west extent.
Distortion of scale, distance, direction and area increase
away from the
central meridian.

Many national grid systems are based on the Transverse
Mercator projection

The British National Grid (BNG) is based on the National
Grid System of
England, administered by the British Ordnance Survey. The
true origin of
the system is at 49 degrees north latitude and 2 degrees
west longitude.
The false origin is 400 km west and 100 km north. Scale at
the central
meridian is 0.9996. The first BNG designator defines a 500
km square. The
second designator defines a 100 km square. The remaining
numeric characters
define 10 km, 1 km, 100 m, 10 m, or 1 m eastings and
northings.

The Universal Transverse Mercator (UTM) projection is used to
define horizontal,
positions world-wide by dividing the surface of the Earth into
6 degree
zones, each mapped by the Transverse Mercator projection with
a central
meridian in the center of the zone. UTM zone numbers designate
6 degree
longitudinal strips extending from 80 degrees South latitude
to 84 degrees
North latitude. UTM zone characters designate 8 degree zones
extending
north and south from the equator.

Eastings are measured from the central meridian (with a
500km false easting
to insure positive coordinates). Northings are measured from
the equator
(with a 10,000km false northing for positions south of the
equator).

Pseudocylindrical Projections

Pseudocylindrical projections resemble cylindrical projections,
with straight
and parallel latitude lines and equally spaced meridians, but
the other
meridians are curves.

Mollweide

The Mollweide projection, used for world maps, is
pseudocylindrical and
equal-area. The central meridian is straight. The 90th
meridians are circular
arcs. Parallels are straight, but unequally spaced. Scale is
true only
along the standard parallels of 40:44 N and 40:44 S.

The Eckert IV projection, used for world maps, is a
pseudocylindrical and
equal-area. The central meridian is straight, the 180th
meridians are semi-circles,
other meridians are elliptical. Scale is true along the
parallel at 40:30
North and South.

The Eckert VI projection , used for maps of the world, is
pseudocylindrical
and equal area. The central meridian and all parallels are
at right angles,
all other meridians are sinusoidal curves. Shape distortion
increases at
the poles. Scale is correct at standard parallels of 49:16
North and South.

The Robinson projection is based on tables of coordinates, not
mathematical
formulas. The projection distorts shape, area, scale, and
distance in an
attempt to balance the errors of projection properties.

Sinusoidal equal-area maps have straight parallels at right
angles to a
central meridian. Other meridians are sinusoidal curves. Scale
is true
only on the central meridian and the parallels. Often used in
countries
with a larger north-south than east-west extent.

Conic Projections

Albers Equal Area Conic

A conic projection that distorts scale and distance except
along standard
parallels. Areas are proportional and directions are true in
limited areas.
Used in the United States and other large countries with a
larger east-west
than north-south extent.

The polyconic projection was used for most of the earlier USGS
topographic
quadrangles. The projection is based on an infinite number of
cones tangent
to an infinite number of parallels. The central meridian is
straight. Other
meridians are complex curves. The parallels are non-concentric
circles.
Scale is true along each parallel and along the central
meridian.

The Lambert azimuthal equal-area projection is sometimes used
to map large
ocean areas. The central meridian is a straight line, others
are curved.
A straight line drawn through the center point is on a great
circle.

Miscellaneous Projections

Unprojected Maps

Unprojected maps include those that are formed by considering
longitude
and latitude as a simple rectangular coordinate system. Scale,
distance,
area, and shape are all distorted with the distortion
increasing toward
the poles.

In 1992, the Cartographic Standards Working Group proposed a
Texas State-Wide
Map Projection Standard for the GIS Standards Committee of the
GIS Planning
Council for the Department of Information Sciences.

Earlier maps had often used projections designed for the
continental United
States

The new projection was designed to allow state-wide mapping
with a minimum
of scale distortion. A Lambert Conformal Conic Projection was
proposed
with an origin at 31:10 North, 100:00 West and with standard
parallels
at 27:25 North and 34:55 North. For plane coordinate use a
false Easting
and Northing of 1,000,000 meters were defined for the origin.

The Space Oblique Mercator is a projection designed to show
the curved
ground-track of Landsat images. There is little distortion
along the ground-track
but only within the narrow band (about 15 degrees) of the
Landsat image.